Periodic orbits in problems with state-dependent delays

Jan Sieber (March 23, 2011)

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Delays in feedback loops tend to destabilize dynamical systems, inducing self-sustained oscillations or chaos. I will show some typical examples in my presentation. I will also show how one can reduce the study of periodic oscillations in systems with delay to low-dimensional smooth algebraic systems of equations. The approach works also when the delay depends on the state, a case in which it is not clear in general if the underlying differential equations are smooth dynamical systems.